Carmelo Anthony fouled out and rookie Kristaps Porzingis’ outing was foul enough that Knicks coach Derek Fisher sat him much of the fourth quarter.

On a night that was a strong indicator the Knicks may not stick around much longer in the playoff race, the Celtics controlled the fourth quarter and pummeled them physically, in a 97-89 statement win at the Garden on Tuesday.

The Knicks have fallen a season-worst five games under .500 at 23-28 and 3 ¹/₂ games out of the eighth seed, losing six of their last seven, leaving owner James Dolan with a sickened look after the game.

If things continue to spiral downward, it will be interesting to see if Knicks president Phil Jackson decides at the trade deadline in three weeks to shop players such as Arron Afflalo, who has an opt-out, Kyle O’Quinn, Jose Calderon and Kevin Seraphin to a playoff-bound team. The Knicks face Detroit next and their backup point guard Brandon Jennings, who is on the block and a free agent in the summer.

“The morale is good,’’ Anthony said. “I don’t think the morale is changing. There is urgency we need to turn this around quickly. The morale and confidence isn’t going anywhere. I won’t allow it but we have to turn this around quickly.’’

Before the game, Fisher said the “process” is more important than playoffs, but the Knicks resembled an outclassed club. Afterward, Fisher pointed out the Celtics are a deeper squad than the Knicks, whose bench was outscored 47-27.

The Knicks also have missed the injured Calderon’s decision-making as the club committed 17 turnovers and shot 37 percent. They weren’t running the triangle offense with any flow — ball movement continuing to be an issue.

Anthony played physically, picking up a flagrant foul on offense for elbowing Jae Crowder while trying to create space. But Anthony shot just 4-of-16 against Crowder’s physicality, had three turnovers and wound up with 16 points and 14 rebounds.

“Personally it was a very bad game for me,’’ Anthony said. “When I’m playing at not at my best, it hurts the team and it showed tonight.’’

It was a low-energy evening for Porzingis, who earlier in the day was named Eastern Conference Rookie of the Month. His February began with a sleepy 10-point, five-rebound night, playing 27 minutes, looking out of place in the physical wars in a second straight dud.

Porzingis will play his 51st game Thursday in Detroit. In last year’s European season in Spain, he played 50 games.

Meanwhile, Boston’s unheralded big man Tyler Zeller smashed the Knicks late and finished with 16 points and 10 rebounds off the bench.

“I had a bad night, missing a couple of shots at the beginning,’’ Porzingis said. “I couldn’t find the rhythm early. Obviously I didn’t help us at all. I wasn’t playing well.’’

“I got him — we’ll put him in the weight room tomorrow,’’ Anthony said jokingly about Porzingis. “He’ll be all right. It is a learning curve. We throw so much on him. He’ll get stronger and get used to it.’’

Porzingis started the fourth quarter but Fisher yanked him after 1:44. He didn’t return until 3:07 remained and the Knicks down 10. Porzingis immediately scored on a floater, but then missed a long 3-pointer that came up short and he got caught not getting back in transition as Boston scored on the fast break.

In explaining the Porzingis benching, Fisher said, “It was a team situation. The third quarter was came out flat, couldn’t figure out way to get anything going. Kristaps played a lot of those minutes. We got him in a for a few minutes to start the fourth and not much was happening for that connection. So it wasn’t about Kris being good or bad, the five guys that were out there just weren’t getting the job done.’’